Državno natjecanje 2006 SŠ3 1
Dodao/la:
arhiva1. travnja 2012. Duljine stranica trokuta su
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,

i

,

. Dokaži da za kutove

i

, nasuprotne stranicama
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i

, vrijedi

.
%V0
Duljine stranica trokuta su $a$, $b$ i $\displaystyle c = \frac{a^2 - b^2}{\sqrt{a^2 + b^2}}$, $a > b$. Dokaži da za kutove $\alpha$ i $\beta$, nasuprotne stranicama $a$ i $b$, vrijedi $\alpha-\beta = 90^{\circ}$.
Izvor: Državno natjecanje iz matematike 2006